I questioned the use of the phrase "real history" because I think it's a
tautology, in much the same way as "true facts". There's no such things
as "false facts," because if they're false, they aren't facts. Similarly,
if it didn't happen, it's not history.

This may be just a matter of taste of my part, but I'd much rather say
"anti-historical" or "a-historical" than "unreal history."